The present disclosure relates generally to an extremum-seeking control (ESC) system. ESC is a class of self-optimizing control strategies that can dynamically search for the unknown and/or time-varying inputs of a system for optimizing a certain performance index. ESC can be considered a dynamic realization of gradient searching through the use of dither signals. The gradient of the system output y with respect to the system input u can be obtained by slightly perturbing the system operation and applying a demodulation measure. Optimization of system performance can be obtained by driving the gradient towards zero by using a negative feedback loop in the closed-loop system. ESC is a non-model based control strategy, meaning that a model for the controlled system is not necessary for ESC to optimize the system.
A plant in control theory is the combination of a process and one or more mechanically-controlled outputs. Traditional ESC systems typically use a periodic (e.g., sinusoidal) dither signal to perturb a control input u provided to the plant. The periodic dither signal can cause large variations (e.g., sinusoidal oscillations) in both the control input u and the plant output y, which are often noticeable to plant operators. Additionally, the frequency of a periodic dither signal needs to be carefully selected to ensure that the ESC strategy is effective. For example, it may be desirable to select a dither signal frequency based on the natural frequency of the plant to enhance the effect of the dither signal on the plant output y. It can be difficult and challenging to properly select the dither frequency without knowledge of the dynamics of the plant. For these reasons, the use of a periodic dither signal is one of the drawbacks of traditional ESC.